Math / Numbers & Operations

QuestionQuestion 13 Next Question
What is the least common multiple of 6,9 , and 12 ? an assignment during this with the unit. (10 points)
Answer $\square$ Submit Answer

Studdy Solution

STEP 1

1. We are tasked with finding the least common multiple (LCM) of the numbers 6, 9, and 12.
2. The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers in the set.

STEP 2

1. Find the prime factorization of each number.
2. Identify the highest power of each prime number that appears in the factorizations.
3. Multiply these highest powers together to find the LCM.

STEP 3

Find the prime factorization of each number.
- $6 = 2 \times 3$ - $9 = 3^2$ - $12 = 2^2 \times 3$

STEP 4

Identify the highest power of each prime number.
- The prime number $2$ appears in $6$ and $12$ . The highest power is $2^2$ . - The prime number $3$ appears in $6$ , $9$ , and $12$ . The highest power is $3^2$ .

STEP 5

Multiply these highest powers together to find the LCM.
$\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36$
The least common multiple of 6, 9, and 12 is:
$\boxed{36}$

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QuestionQuestion 13 Next Question
What is the least common multiple of 6,9 , and 12 ? an assignment during this with the unit. (10 points)
Answer $\square$ Submit Answer

Studdy Solution

STEP 1

1. We are tasked with finding the least common multiple (LCM) of the numbers 6, 9, and 12.
2. The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers in the set.

STEP 2

1. Find the prime factorization of each number.
2. Identify the highest power of each prime number that appears in the factorizations.
3. Multiply these highest powers together to find the LCM.

STEP 3

Find the prime factorization of each number.
- $6 = 2 \times 3$ - $9 = 3^2$ - $12 = 2^2 \times 3$

STEP 4

Identify the highest power of each prime number.
- The prime number $2$ appears in $6$ and $12$ . The highest power is $2^2$ . - The prime number $3$ appears in $6$ , $9$ , and $12$ . The highest power is $3^2$ .

STEP 5

Multiply these highest powers together to find the LCM.
$\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36$
The least common multiple of 6, 9, and 12 is:
$\boxed{36}$

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QuestionQuestion 13 Next QuestionWhat is the least common multiple of 6,9 , and 12 ? an assignment during this with the unit. (10 points)Answer □\square□ Submit Answer

Studdy Solution

STEP 1

1. We are tasked with finding the least common multiple (LCM) of the numbers 6, 9, and 12.2. The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers in the set.

STEP 2

1. Find the prime factorization of each number.2. Identify the highest power of each prime number that appears in the factorizations.3. Multiply these highest powers together to find the LCM.

STEP 3

Find the prime factorization of each number.- 6=2×3 6 = 2 \times 3 6=2×3 - 9=32 9 = 3^2 9=32 - 12=22×3 12 = 2^2 \times 3 12=22×3

STEP 4

Identify the highest power of each prime number.- The prime number 2 2 2 appears in 6 6 6 and 12 12 12. The highest power is 22 2^2 22. - The prime number 3 3 3 appears in 6 6 6, 9 9 9, and 12 12 12. The highest power is 32 3^2 32.

STEP 5

Multiply these highest powers together to find the LCM.LCM=22×32=4×9=36\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36LCM=22×32=4×9=36 The least common multiple of 6, 9, and 12 is:36\boxed{36}36​

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QuestionQuestion 13 Next Question
What is the least common multiple of 6,9 , and 12 ? an assignment during this with the unit. (10 points)
Answer $\square$ Submit Answer

1. We are tasked with finding the least common multiple (LCM) of the numbers 6, 9, and 12.
2. The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers in the set.

1. Find the prime factorization of each number.
2. Identify the highest power of each prime number that appears in the factorizations.
3. Multiply these highest powers together to find the LCM.

Find the prime factorization of each number.
- $6 = 2 \times 3$ - $9 = 3^2$ - $12 = 2^2 \times 3$

Identify the highest power of each prime number.
- The prime number $2$ appears in $6$ and $12$ . The highest power is $2^2$ . - The prime number $3$ appears in $6$ , $9$ , and $12$ . The highest power is $3^2$ .

Multiply these highest powers together to find the LCM.
$\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36$
The least common multiple of 6, 9, and 12 is:
$\boxed{36}$